Yes, the AE-1 can do multiple exposures but not easily. You have to rewind the film and wind again since there is no way to cock the shutter without winding and there is no dedicated multiple exposure feature. You need to rewind and look at the little dot on the rewind button to get the spacing right. Not easy to do but it is what he has so you have to work with what you've got.

You could 'black hat' it though, put it on a tripod and cover the lens with a 'hat' and take it off for seconds at a time during totality, replacing the 'hat' each time. At the darkest point of totality it may take 30s for the exposure which will be blurred but that's what you get unless you have a driven mount.

I had never thought of the hat trick (new use for that term!) and that is quite brilliant.

One other technique I was told about long long ago by a film class instructor (when discussing my AE-1 Program I used in-class) was as follows: You can take up all the tension on the rewind spool, hit the "film rewind" button underneath, then advance the film lever. Thus keeping the film in place and recocking the shutter.

I've never had the guts/imagination to try it (my subjects are far more ordinary), but I would be careful how much tension you put on the rewind lever. Too much, and it might "spring back" a bit when you pop the rewind button.

He was a pretty smart instructor. He knew some tips and tricks that I've never tried myself, and it was clear he loved film.